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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 90354o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
90354.n2 | 90354o1 | \([1, 1, 1, 6132, 2008509]\) | \(13605635375/935384208\) | \(-1753060602649488\) | \([]\) | \(508032\) | \(1.6046\) | \(\Gamma_0(N)\)-optimal |
90354.n1 | 90354o2 | \([1, 1, 1, -4662158, -3880171573]\) | \(-5979677811120816625/6457751764992\) | \(-12102866505629171712\) | \([]\) | \(3556224\) | \(2.5775\) |
Rank
sage: E.rank()
The elliptic curves in class 90354o have rank \(1\).
Complex multiplication
The elliptic curves in class 90354o do not have complex multiplication.Modular form 90354.2.a.o
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.